Every once in a while The Android messaging app will seem to stop. It will display "No Conversations", There should be messages / conversations to be display. When this happens I will not be able to send or receive messages. If I power down the phone and then restart, the missing conversations reappear. I am then able to send and receive text messages.

Welcome to Android Central! Have you tried using Hangouts for SMS? Even if you don't like Hangouts, it may be a good way to figure out if it's the Messaging app that's the problem, or your phone's overall SMS functionality.

Try going to Settings>Apps>All, select Messaging, and Clear Cache/Clear Data, then Force Stop. See if the problem recurs. Be aware that Clear Data might delete any texts you're trying to save (but I'm not certain of this).

I have select clear cache and clear data. Then tried to receive a message from another phone, it was not received. I powered down and powered up the nexus 4 and the problem went away. But it came back a few days later.